GREGORY, DUNCAN FARQUHARSON (1813–1844), mathematician, born at Edinburgh in April 1813, was the youngest son of James Gregory (1753-1821) [q. v.], professor of medicine in the university of Edinburgh. Till he was nine years old he was taught entirely by his mother; in October 1825 he was sent to the Edinburgh Academy, and after two years there spent a winter at a private academy at Geneva. As a child he displayed great powers in acquiring knowledge, as well as ingenuity in mechanical contrivances (such as making an orrery), and at Geneva his mathematical talent attracted attention. On his return he attended classes at the Edinburgh University, working at chemistry, making experiments in polarised light, and advancing in the higher parts of mathematics, under the tuition of Professor Wallace. In October 1833 he commenced residence at Trinity College, Cambridge, where he took the degrees of B.A. in 1838 and M.A. in 1841; he came out as fifth wrangler in the tripos of 1837, and was elected fellow of Trinity in October 1840. He served the office of moderator in 1842, and was appointed assistant tutor of his college. Soon after taking his degree he was one of the projectors and the first editor of the ‘Cambridge Mathematical Journal,’ and many of the most valuable of its papers are from his pen. These have been collected in a volume, under the title ‘The Mathematical Writings of D. F. Gregory,’ edited by his friend Mr. W.Walton, Cambridge, 1865. In 1841 he published his ‘Examples of the Processes of the Differential and Integral Calculus,’ a work which produced a great change for the better in the Cambridge mathematical books. It is the first in which constant use is made of the method known by the name of the separation of the symbols of operation, and the author has enlivened its pages by occasionally introducing historical notices of the problems discussed. A second edition appeared after his death in 1846 under Mr. Walton's editorial care. His other mathematical work was ‘A Treatise on the Application of Analysis to Solid Geometry,’ which was left unfinished at his death, and was completed and published by Walton in 1845. This is the first treatise in which the system of solid geometry is developed by means of symmetrical equations, and is a great advance on those of Leroy and Hymers. A second edition appeared in 1852.

Though his time was chiefly employed on mathematical subjects, this was by no means his only branch of study; he was an able metaphysician, a good botanist, and was so well acquainted with chemistry that he occasionally gave lectures on chemical subjects, and acted for some time as assistant to the professor of chemistry. He was at one time a candidate for the mathematical chair at Edinburgh; in 1841 he refused that at Toronto. His health gave way in 1842, and after great suffering he died at Canaan Lodge, Edinburgh, on 23 Feb. 1844.